If A is a square matrix such that A2 = I, then find the simplified value of (A -1)3 + (A +1)3 – 7A.
Find the differential equation representing the family A of curves Ï… = A/r + B, where A and B are arbitrary r constants.
Two schools P and Q want to award their selected students on the values of Discipline, Politeness and Punctually. The school P wants to award Rs x each, y each and Rs z each for the three respective values to its 3,2 and 1 students with a total award money of Rs 1,000. School Q wants to spend Rs 1,500 to award its 4,1 and 3 students on the respective values (by giving the same award money for the three values as before). If the total amount of awards for one prize on each value is Rs 600, using matrices, find the award money for each value. Apart from the above three values, suggest one more value for awards.
A dealer in rual area wishes to purchase a number of sewing machines. He has only Rs 5,760 to invest and has space for at most 20 items for storage. An electronic sewing machine cost him Rs 360 and a manually operated sewing machine Rs 240. He can sell an electronic sewing machine at a profit of Rs 22 and a manually operated sewing machine at a profit of Rs 18. Assuming that he can sell all the items that he can buy, how should he invest his money in order to maximize his profit ? Make it as a LPP and solve it graphically.
A manufacturer produces two products A and 6. Both the products are processed on two different machines. The available capacity of first machine is 12 hours and that of second machine is 9 hours per day. Each unit of product A requires 3 hours on both machines and each unit of product B requires 2 hours on first machine and 1 hour on second machine. Each unit of product A is sold at Rs 7 profit and B at a profit of Rs 4. Find the production level per day for maximum profit graphically.
If a line makes angles 90 °, 60 ° and θ with x, y and z axis respectively, where θ is acute, then find θ.
Solve the differential equation: (tan-1 y-x)dy = (1 + y2) dx.
Solution. Same as solution Q. 23 (OR) Set 1 (Outside Delhi) up to eq.
x = tan-1 y -1 + ce -tan-1 y
OR
Three persons A, B and C apply for a job of Manager in a Private Company. Chances of their selection (A, B and C) are in the ratio 1:2:4. The probabilities that A, B and C can introduce changes to improve profits of the , company are 0.8,0.5 and 0.3 respectively. If the change does not take place, find the probability that it is due to the appointment of C.
Three Schools A, B and C organized a mela for collecting funds for helping the rehabilitation of flood victims. They sold hand made fans, mats and plates from recycled material at a cost of Rs 25, Rs 100 and Rs 50 each. The number of articles sold are given below:
Find the fund collected by each school separately by selling the above articles. Also find the total funds collected for the purpose. Write one value generated by the above situation.
The monthly incomes of Aryan and Babban are in the ratio 3:4 and their monthly expenditures are in the ratio 5:7. If each saves Rs 15,000 per month, find their monthly incomes using matrix method. This problem reflects which value?
Find the intervals in which f(x) = sin 3x – cos 3x, 0 < x < Ï€, is strictly increasing or strictly decreasing.
A bag ‘A’ contains 4 black and 6 red balls and bag ‘B’ contains 7 black and 3 red balls. A die is thrown. If 1 or 2 appears on it, then bag A is chosen, otherwise bag B. If two balls are drawn at random (without replacement) from the selected bag, find the probability of one of them being red and another black.
An unbiased coin is tossed 4 times. Find the mean and variance of the number of heads obtained.
If A is a square matrix such that A2 = I, then find the simplified value of (A -1)3 + (A +1)3 – 7A.
Find the vector equation of a plane which is at a distance , of 5 units from the origin and its normal vector is
